Controlling Cell Motion and Microscale Flow with Polarized Light Fields

We investigate how light polarization affects the motion of photoresponsive algae, Euglena gracilis. In a uniformly polarized field, cells swim approximately perpendicular to the polarization direction and form a nematic state with zero mean velocity. When light polarization varies spatially, cell motion is modulated by local polarization. In such light fields, cells exhibit complex spatial distribution and motion patterns which are controlled by topological properties of the underlying fields; we further show that ordered cell swimming can generate directed transporting fluid flow. Experimental results are quantitatively reproduced by an active Brownian particle model in which particle motion direction is nematically coupled to local light polarization.

Figure 1

Cell motion in a uniformly polarized light field. (a) Cell trajectories (color coded by time) plotted on an experimental snapshot. Light polarization is horizontal and cells tend to swim vertically in the targeted direction ${\theta }_T$. (b) shows a schematic for a cell (with a red eye spot and a flagellum) which moves at a $\phi$ direction; a circular arrow indicates body rolling motion. (c) Probability distribution of cell motion direction $\phi$.

Figure 2

Orientation, velocity, and cell density in axisymmetric light fields containing a $k=+1$ defect with ${\theta }_0=\pi /2$ (a),(c) and ${\theta }_0=3\pi /4$ (b),(d). In (a),(b) targeted direction ${\theta }_T$ and mean cell motion direction ${\varphi }_u$ are shown by green and black lines, respectively, on nematic order parameter $u$ (in color). In (c),(d) mean cell velocity $\overrightarrow{v}$ is plotted on mean density (in color). In (a)–(d), top and bottom halves (separated by a white line) are experimental and numerical results, respectively. The inset of (b) defines three angles (see text). (e)–(g) Radial profiles of nematic order parameter $u$, tangential velocity $v_t=\overrightarrow{v}·\widehat{\varphi }$, and cell density $\rho$ for four fields.

Figure 3

(a) Mean angular velocity $\dot{\phi }$ versus the angular deviation $\phi -{\theta }_T$ in in axisymmetric light fields. The inset shows effective diffusivity $D$ measured in different fields ${\theta }_0$. (b)–(g) Deterministic trajectory and probability distribution in axisymmetric fields with ${\theta }_0=\pi /2$ (b),(d),(f) and ${\theta }_0=3\pi /4$ (c),(e),(g). (b),(c) Cell trajectories from the deterministic model plotted on the targeted field. See Fig. S8 [56] for more trajectories. (d),(e) Experimentally measured probability $p(r,{\phi }_d)$ (color) and computed phase trajectories (black lines). Stable and neutrally stable fixed points are colored in red. Fixed points in (d) are outside of the experimentally measured range ($r<10.8\mu \mathrm{m}$). (f),(g) Profiles of $p(r,{\phi }_d)$ at three radii. Dashed lines in (d),(g) mark targeted direction ${\theta }_T$.

Figure 4

Trajectories of passive tracers (top panel, from experiments) and flow field (bottom panel, from the dipole model) driven by Euglena in a light field with $k=+1$ and ${\theta }_0=\pi /4$. An experimental snapshot is shown in the background. The inset shows radial profiles of tracers tangential velocities in three axisymmetric ($k=1$) light fields.

Figure 5

Orientation (a) and velocity or density (b) in a light field containing a $k=-2$ defect with ${\theta }_0=\pi /2$. In (a), targeted direction ${\theta }_T$ and mean cell motion direction ${\varphi }_u$ are shown by green and black lines, respectively, on nematic order parameter $u$ (in color). In (b), mean cell velocity $\overrightarrow{v}$ is plotted on mean density (in color). Top and bottom panels are experimental and numerical results, respectively.